Correct BS for pair of 9's vs. Ace in SD, H17 game??

The website that says you should always split 9's vs. Ace in a SD, H17 game is thewizardofodds.com, not wizardofodds.com, as I originally indicated. I've provided the link to it in this post.

this may be the most debatable basic strategy situation there is!

You said: "you should split, except if you can split only once"

From a logical point of view this sounds rather bizarre.
Provided a splitting decision is wrong in the first place, how can it become better by repeating the same mistaken option.

Francis Salmon

It should be noted, that the Black Jack Advocate uses estimations for calculating the splitting decisions (and calculates exact otherwise). The reason is the multitude of card that could be drawn. As there are not so much cards that could be drawn for high cards to split such as 9/9, it should be easy and fast to calculate the correct values in these cases, I am still working on that.
The deviation of my estimations of the expected values of the Splitting Decisions from the correct values should not exceed 1%, but this would be enough in this case to give an incorrect advise.
The probability of having 9/9 vs Ace is 0.0362%, and your maximum favor in ev (using Black Jack Advocate) is around 0.35%. So your overall favor would be max around 0.0001%.
(I agree with Parker, that this is a bad justification to double or triple the maximum loss, although it might be the better decision in a long run.)

Perhaps my words have been not precise enough due to my bad english. I did not say, that the first split is wrong, and a second one would be right, I say, that the first split is wrong ONLY IF table rules do not allow a second split, and the first split is right ONLY IF table rules do allow a second (and third) split.

That could be, because if you draw a third nine, the probability to draw Tens after that increase. By splitting again you can use these favors for all your three hands, if you are in opposition forced to stand with your 18... (this explaination is rather incomplete, but can give you the right direction, that such bizarre phenomen could occur. Take into account that the differences in the expected values of standing resp. Splitting in that case are very, very small)
I want to add that I didn't calculated this exactly. Please read my "note" posting too.

After reading this entire thread, and consulting ALL the web sites and texts mentioned, I have come to the following conclusion: I still don't know the answer to Cincinnati Kid's question!

Don, it does appear that Griffin's and the wizard's charts disagree. My vote goes to Griffin, given the vaguaries associated with pair splitting algorithms. Wong's Appendix E also concurs with Griffin that the only time it's basic to split 99 v A is with 1D H17 DAS.

BUT, I can't use Wong to confirm because there is a mistake in Wong's logic on pair splitting! On p. 300 of Professional Blackjack Wong writes "If splitting is the best way to play a pair, the tables will say so no matter whether the calculations assume no replits, unlimited resplits, or something in between." This might be true, but it isn't tautological, as Wong seems to assume. Wong's tables assume no resplits. As Graenzer points out above, it's possible for splitting to be incorrect under no resplit conditions, yet become correct when resplitting is allowed.

It is true that if splitting is recommended by Wong's tables then basic strategy will also say to split, but that isn't quite the same thing! Therefore, it is just conceivable that resplitting could improve the EV for splitting 99 v A from -.193 to -.186 or more, so basic would then be to split the pair under 1D H17 NoDAS.

So, to summarize, I believe that Griffin is probably correct when he says basic is to split 99 v A ONLY with 1D H17 and DAS, and I'd say if the wizardofodds has proof to the contrary, he should come forward from behind the curtain! I also agree with MathProf that splitting 99 v A is good "counter's bs," while at the same time agreeing with Parker that standing is the risk averse way to go.

ETF

By sense form Griffin is that BS is to split only when you have SD-H17 and Das. I did not see this qualification in Shackleford's site; it looked to me like he was recommending it in for all single-deck game.

I have not see a lot of single deck games that allow DAS. So I think that someone who gives a DAS strategy for SD, and treats it as the generic SD strategy, should be considered "wrong".

Some have asked about Risk Aversion. It would be interesting to compute the RA indexes for this play. My guess is that they are low enough to make this CBS.

I have really grown quite fond of CBS. I think it may be the most important concepts in BJ to have come along recently.

I would be happy to discuss this play, or these issue further, on Green Chip.

In his appendix 9b, Mike has the right probabilities.

http://www.thewizardofodds.com/game/bjapx9b.html

Ignore the top chart, which, erroneously, says "Hands which may be split." He meant to write, "Which may NOT be split." Use the second chart. Clearly, he knows the right plays!

The color-coded chart should have a "H/P" designation, instead of the plain "P." I'll tell him.

Don

Mike's numbers agree precisely with Wong's. Go by Mike's appendix 9b, and not his color-coded chart.

I'm going to contact Steve Jacobs with this, and we'll get a precise answer.

Don

"The color-coded chart should have a "H/P" designation, instead of the plain "P." I'll tell him."

Correction!! The chart should read "S/P," but he has no such designation! Maybe that's the problem. This is a unique hand!

Don

I consider Steve Jacobs and Mike Shackleford to be two of the foremost combinatorial analysts we have today in the field. I think Cacarulo is the third, but I don't have his e-mail address! Here is my letter. In the meantime, I'm going to check over at bjmath. There may be something there, as well.

Don

Steve,

How are you? Hope all is well. There's a fine point of BS discussion going on on bj21, and I thought I'd solicit some input from you.

For SD, H17, it appears, from Griffin, p. 173, and from Wong's appendixes, that splitting nines vs. ace is correct only when DAS is permitted. Apparently, the EV for splitting with das is -0.185+, while the EV for standing is -0.186. However, with no das, the EV for splitting drops to -0.193+, and standing is now the correct BS play.

Mike, your Appendix 9B indicates this clearly, but your SD H17 BS chart is wrong, because you give "P," as if pair-splitting were always correct, when you should be giving "S/P," which doesn't exist in your legend. This is a unique hand! Also, Mike, your top chart in 9b says "Hands Which May Be Split," when you mean "May Not." Have you done this with all of the double charts? You'd better check!

Back to Steve: Now, to make matters interesting, someone has hypothesized that maybe the -0.193 for no DAS is correct only when a single split is permitted, and that, when two or three splits are permitted, the EV improves to a point where it may be superior to standing, even with no DAS. Although I doubt this very, very much, I wonder if you would take a look, please. Note that Griffin does NOT recommend splitting for this play if no DAS. But, it's worth checking him, right Steve?! :-)

Thanks.

Regards,

Don

For 1D,H17,NDAS,SPL3 ==> STAND

Standing  =  -18.613048871482%

Splitting =  -19.123133032238%



For 1D,H17,DAS,SPL3 ==> SPLIT



Standing  =  -18.613048871482%

Splitting =  -18.393964186334%



Hope this answers your question.



Sincerely,

Cacarulo







                

bjmath.com has provided our answer, courtesy of Cacarulo. He does NOT do SD, H17, DAS, but he does do SD, H17, NDAS, split to four hands. And the EV for splitting is -0.19123, not even close to the -0.1861 EV for standing.

General rule: the EV from resplits would NEVER change by as much as we were asking it to, in this situation.

So, to recap: Griffin is 100% right, as always (!). Mike is right, if you look at his numerical charts, and not his color charts. Wong's appendixes are right, for no resplits. It remains to be seen if any BS play actually changes because the EV from one split to three splits actually straddles the alternative decision. My guess would be no, but in any event, we know for certain that it does not affect THIS play.

Game, set, match. Case closed!

Don

If you actually have text in your post, and want people to read the content, don't add "nt" to the end of your title! :-)

Now, ask me why I was "dumb" enough to open the post anyway! :-)

Don

I was so wrapped up in going over to bjmath and writing to the two guys, I missed your post here, Cac!

Great work!

Note that the EVs for splitting vs. standing, when DAS is permitted, aren't as close with three splits allowed as with only one. Since the former is, by far, much more common, the play really isn't all that close, after all.

Don

then:

1D,H17,NDAS,SPL1 ==> STAND

Standing  =  -18.613048871482%

Splitting =  -19.282770194668%

Standing  =  -18.613048871482%

Splitting =  -18.597113065038%

SBA says that the risk-averse HO2 index for splitting 9,9 against
a dealer ace SD H17 NDAS is +7.

I was wondering about the statement:

I consider Steve Jacobs and Mike Shackleford to be two of the foremost combinatorial analysts we have today in the field. I think Cacarulo is the third, but I don't have his e-mail address!

I am not trying to take anything away from Steve or Mike, but how do rate Cac. As third? Is there some objective criterion? Some analysis that Steve does better than Cac.

I know a little bit about Steve, and more about Cac. They both seem to be fine programmers, and I wouldn't be able to rate one above the other.

being around long enough to get a strong reputation. Cacarulo's reputation gets stronger every day.

I know Steve for years. Then came Mike. Finally Cac. It's not a question of a contest. I'd swear by any of the three of them!

Don